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A Union Self-evaluation Approach to Associated Consistency for Cooperative Games

Author

Listed:
  • Wenzhong Li

    (Northwestern Polytechnical University
    International Joint Research Center on Operations Research, Optimization and Artificial Intelligence
    Northwestern Polytechnical University)

  • Genjiu Xu

    (Northwestern Polytechnical University
    International Joint Research Center on Operations Research, Optimization and Artificial Intelligence)

  • René van den Brink

    (International Joint Research Center on Operations Research, Optimization and Artificial Intelligence
    VU University)

Abstract

Xu et al. (Linear Algebra Appl 430(11):2896–2897, 2009) introduced the notion of associated consistency according to the idea of “individual self-evaluation". In this paper, we introduce a new type of associated consistency according to the idea of “union self-evaluation" instead of “individual self-evaluation". Adopting this type of associated consistency, we provide new axiomatizations of the equal allocation of non-separable contributions (EANSC) value and the center-of-gravity of the imputation set (CIS) value. Moreover, a dynamic process is given based on the type of associated games, which leads to the CIS value and EANSC value, starting from an arbitrary efficient payoff vector.

Suggested Citation

  • Wenzhong Li & Genjiu Xu & René van den Brink, 2023. "A Union Self-evaluation Approach to Associated Consistency for Cooperative Games," Journal of Optimization Theory and Applications, Springer, vol. 199(3), pages 863-880, December.
    • Handle: RePEc:spr:joptap:v:199:y:2023:i:3:d:10.1007_s10957-023-02322-0
    DOI: 10.1007/s10957-023-02322-0
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